Posted by SUPER HARD on Sunday, November 25, 2012 at 8:21am.
You have a right-angled triangle so we can use the formula
(1/2) base x height
Since you want the answer as a common fraction, I will assume that you need "exact" values.
you state that BC = \sqrt{3}
I will assume that is meant to say √3
so cos75 =base/√3
base = √3cos75
and sin75 = height/√3
height = √3sin75
area = (1/2)(√3sin75)(√3cos75)
= (3/2)sin75cos75)
(recall sin 2A = 2sinAcosA)
= (3/2)(2sin75cos75)/2
= (3/4) sin 150
sin 150 = sin30 ---- one of the basic identities
area = (1/3) sin150
= (3/4)sin30
= (3/4)(1/2) = 3/8
thanks alot
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